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Problem of the day

Given an array “A” of N integers and you have also defined the new array “B” as a concatenation of array “A” for an infinite number of times.

For example, if the given array “A” is [1,2,3] then, infinite array “B” is [1,2,3,1,2,3,1,2,3,.......].

Now you are given Q queries, each query consists of two integers “L“ and “R”(1-based indexing). Your task is to find the sum of the subarray from index “L” to “R” (both inclusive) in the infinite array “B” for each query.

Note :

```
The value of the sum can be very large, return the answer as modulus 10^9+7.
```

Detailed explanation

```
1 <= T <= 100
1 <= N <= 10^4
1 <= A[i] <= 10^9
1 <= Q <= 10^4
1 <= L <= R <= 10^18
Time Limit: 1sec
```

```
1
3
1 2 3
2
1 3
1 5
```

```
6 9
```

```
For the first test case, the given array A is [1,2,3] therefore the infinite array “B” will be [1,2,3,1,2,3,1,2,3,.......]. So the answer for the given first query is 6 because the sum of the subarray from index 1 to 3 of infinite array “B” i.e. (B[1]+B[2]+B[3]) is 6.
For the given second query is 9 because the sum of the subarray from index 1 to 5 of array “B” .ie (B[1]+B[2]+B[3]+B[4]+B[5]) is 9.
```

```
1
4
5 2 6 9
3
1 5
10 13
7 11
```

```
27 22 28
```